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| Brackets | Equations with Brackets | Double Brackets |
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Brackets
Brackets are used to group terms together.
If we want to remove brackets, then everything inside the bracket must be multiplied by the term on the outside.
3 (y + 2) = 3 x y + 3 x 2 = 3y + 6
Both y and the + 2 must be multiplied by 3.
5 (y – 3) = 5 x y – 5 x 3
= 5y – 15
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Equations with Brackets
Example 1: solve 5 (y – 3) = 20
Remove the brackets
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5y – 15 = 20 |
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5y = 20 + 15 |
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5y = 35 |
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y = 35 divided by 5 |
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y = 7 |
| Example 2: solve |
p + 4 = 5 |
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Note: this line brackets p + 4 together. So we cannot (- 4) first.
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p + 4 = 5 |
(multiply by 3)
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p + 4 = 5 x 3
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p + 4 = 15
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(– 4 from both sides) |
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p = 15 – 4
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p = 11 |
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Double Brackets
Example 1:
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| (y + 3)(y + 2) = y(y + 2) + 3(y + 2) |
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= y2 + 2y + 3y + 6
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= y2 + 5y +6
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Note: we multiply the second bracket by y and then by 3.
Example 2:
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| (y + 5)(y - 2) = y(y - 2) + 5(y - 2) |
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= y2 - 2y + 5y - 10
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= y2 + 3y - 10
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Example 3:
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(x - 3)(x - 4) = x(x - 4) - 3(x - 4)
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= xx - 4x - 3x + 12
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= x2 - 7x + 12
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Note: this time we multiply by -3. This changes the signs in the second bracket. |
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